International workshop on theory of many-body problems

Interacting many-body systems are characterized by correlation functions with a hierarchical structure. Standard theories of interacting electrons, classical liquids, and nonequilibrium dynamics are related to such hierarchical structures. Data-driven methods have recently attracted attention as an approach to solving the hierarchical equations. Here, we organize an international workshop to exchange ideas and methods developed in various fields, with the aim of achieving breakthroughs.

1. Exchange-correlation functionals of electrons
   
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   Many-electron systems are characterized by a two-body correlation function called the exchange-correlation kernel in the Kohn-Sham (KS) density functional theory (DFT).This functional can be obtained by machine learning the electronic structure of accurately solvable systems such as small molecules and non-formed electron systems. This workshop will focus on recently developed methods. However, if possible, it is desirable to obtain information on the correlation of the entire n-body, not just two bodies. Quantum Monte Carlo simulations and dynamical mean field theory (DMFT) can play a complementary role, for example, when multiple electrons in the d- or f-shell of an atom are strongly correlated. The functional renormalization group was developed as a new alternative to KS DFT. This workshop will also focus on such methods and possible extensions based on machine learning.

2. Statistical theory of classical fluids
   
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   The theory of classical fluids has been developed by representing the grand potential as a functional of the external potential, or equivalently, by representing the free energy as a functional of the particle density.The functional can be characterized by the BBGKY hierarchy of correlation functions. The hierarchy can be formulated by a continuous modification of the interparticle interaction, by rescaling the length and energy scale, and so on. In this workshop we will focus on the hierarchical structure in addition to the machine learning approach to solving the hierarchical equations. We will also discuss the relationship between the conventional method based on the classical statistical approach and the renormalization group method based on the quantum field theory.

3. Functionals in quantum master equations
   
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   Hierarchical structure appears in the quantum master equation as well.There is a way to solve the hierarchical equations numerically exactly, and in addition, machine learning approach has been developed trying to accelerate the computation. In this workshop we learn from this successful case and discuss if a similar approach may be applied to other hierarchies.

4. Machine learning approaches
   
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   Machine learning is a common tool that concerns every branch of the hierarchy.It has been utilized for representing complicated functionals in the theories, as well as developing practical approximations that efficiently apply to the system of user’s interest. We discuss current state-of-the-art usages of the machine learning and also explore its novel applications.

5. Other topics, concerning DFT and more general many body problems
   
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   We pursue cross sections of the DFT and more sophisticated many body methods, that includes
   -DFT for composites: superconductors, nuclear matter, etc.
   -Green’s function methods for first-principles calculations
   -Efficient numerical algorithms
   -Quantum computation
   -etc.

Invited Lecturers

Kieron Burke (UC Irvine)　Sam Vinko (U Oxford)　Matthias Schmidt (U Bayreuth)　Karsten Held (TU Wien)　Junren Shi (Peking U)　Yoshitaka Tanimura (Kyoto U)　Tomoaki Yagi (RIKEN)　Kiyoharu Kawana (Seoul Nat’l U)　Hiroshi Shinaoka (Saitama U)

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